Interpreting a formula for Blender Python
With numpy
An ideal candidate for using numpy  For example, can define a sequence
&gt;&gt;&gt; x = np.arange(5)
&gt;&gt;&gt; x
array([0, 1, 2, 3, 4])

and run a function quickly over all items, simple example squaring them.
&gt;&gt;&gt; np.power(x, 2)
array([ 0,  1,  4,  9, 16])

Halving and squaring
&gt;&gt;&gt; np.power(x / 2, 2)
array([0.  , 0.25, 1.  , 2.25, 4.  ])

The question equation.
Test script, defines a function of $x$ with scalars (assume they're scalars) $L$ and $c$
import bpy
import numpy as np

def distribute(x, L, c):
    return L * np.power(x / L, 1 / c)

# test run

x = np.arange(20)
for d in distribute(x, 10, 2):
    bpy.ops.object.empty_add(location=(d, 0, 0))


Empties placed as result of test run.
Related.
Create curve from Numpy Array using Python